As F451 says, this is nothing new. I'm not sure if Shapps is utterly ignorant or just shameless but in the spirit of rehashing old ideas, I'll re-jig the comment I posted last year:
The Housing Act gave social tenants the right to exchange tenancies in 1985, and thousands of them take place every year.
These were previously facilitated by HOMES, which ran a national mutual exchange register called Homeswap among other projects designed to help tenants move more freely to areas of their choice.
It was decided in 2007 that Homeswap was too inefficient, so it was closed and a private company was given a large amount of public money to modernise the service and relaunch it as MoveUK. It failed to do so, and shortly after the project was discontinued, the company announced (entirely by coincidence, undoubtedly) their own, for profit, exchange service.